8.28 Coursera Regression Models Quiz 2 Question 9

Question 9 states the following:

Refer back to the mtcars data set with mpg as an outcome and weight (wt) as the predictor. About what is the ratio of the the sum of the squared errors, ∑ni=1(Yi−Y^i)2 when comparing a model with just an intercept (denominator) to the model with the intercept and slope (numerator)?

I am confused about the term numerator and denominator.

Michele Coleman's comment:

Yukai: the use of "numerator" and "denominator" are very specific to this question and not applicable to regression models in general.

In this question the word denominator  refers to the phrase "a model with just an intercept" and the word numerator refers to the phrase "the model with the intercept and slope".

The question is asking you to compare two different models by calculating the ratio of the sum of squared errors. You are asked to find A / B, where A = the sum of squared errors for model 1. B = the sum of squared errors for model 2, where model 1 has a slope and an intercept and model 2 has just an intercept.

A/B 
= (the sum of squared errors for model 1) / (the sum of squared errors for model 2)

= the sum of squared errors for the model with an intercept and slope) / (the sum of squared errors for the model with just an intercept)